It depends on your LinkedIn subscription:
• Premium Career: 5 per month (max 15 stored)
• Premium Business: 15 per month (max 45 stored)
• Sales Navigator Core: 50 per month (max 150 stored)
• Recruiter Lite: 30 per month (max 120 stored)
If you reach your storage limit, unused InMails will stop rolling over until you send some